55 % 
3-5 7-9-5/ 
Mr. Hellins's improved Solution of 
3-5-7. 9-H-7/ 
_L 
4.6.8.10.6.4 * 
which equation, in fluxions, gives 
35 7-9- 11 -»3*9 / 
+ j j / ‘y * r •> 
4 6.8.10.12.14.10.8 9 
5-7 » 7-5 . 5-3 
12/ 
* 12 V 6 I 
*2/ 
12/ 
+ 
+ (- 
5-7 
123 s 
16/ 
7-4 
12 / 
3 
8 / 
3-5 
5.2 
+ « 
8 / 
-L.X_ 
* 163 
8/ 
+ 
+ 
i6yy 
5 
16^3 
3 
32 / 
3 
>• 
0. 
+ 
67 
192.73 
5 
— WJ/ 
105 
9 
8/ 
+ 
5 
l6yy 
512 
\y — 
8 y 4 1633 
3 -S‘ 7 - 9 - 5 - 3 y yy _r 3-5-7 -9-H-7-533 4 
4.6.8.10.6.4 * 4.6.8.10.12.8.6 
And this equation, more concisely expressed, and divided by y 9 
gives , 
! 3-5-7-9- I ^- I 3-9-7i/ eg 
*"* 4.6.8.10.12.14.10.8 9 
y I 35 r _5 JL_1 • [ 9 1 
Q_\I2/‘T“ 12/ 4831 s 16// \ 83 s * 
+7(— rff; — 
5 
1 63 s 
+ 
*5 
8 /' 
3.5.7.9.11.7.533 
323 s 1 1923 
+ 
5123 
3.5.7.9.11.13.9.733 s 
I 23 9 
3-S-7-9-5-333 
4.6.8.10.6.4 1 4.6.8.10.12.8.6 * 4.6.8. 10. 12. 14. 10.8 
Now the fluent of the fluxionary series on the second side 
of the equation being obviously the series " + 
3^57.9. 11.7.53* 3-5 7-9-1 1- 1 3-9-7/ eg t f .a 
4.6.8.10.12.8 6.4 * 4.6. 8. 10.12. 14.10. £.6’ ^ €m We are neXt t0 taxe late 
fluent of the expression on the first side, and to correct it, that 
it may be = this series ; which may be done as follows ; 
For the fluent sought, assume 
b , c , d \ , 1 f r g 
a 
+ 
a 
P 
+ 1“ “ET~ + 
yy 
s 
+ U 
4- — {- h 
I V V * 
yy 
+ “ + “ + “ + t L . y, and take the fluxion 
of this expression, which will be 
